Core-free, rank two coset geometries from edge-transitive bipartite graphs

Year, pages: 2014, 991 - 1006

It is known that the Levi graph of any rank two coset geometry is an edge-transitive graph, and thus coset geometries can be used to construct many edge transitive graphs. In this paper, we consider the reverse direction. Starting from edge-transitive graphs, we construct all associated core-free, rank two coset geometries. In particular, we focus on 3-valent and 4-valent graphs, and are able to construct coset geometries arising from these graphs. We summarize many properties of these coset geometries in a sequence of tables; in the 4-valent case we restrict to graphs that have relatively small vertex-stabilizers.

Saedeleer, J., Leemans, D., Mixer, M., Pisanski, T. 2014. Core-free, rank two coset geometries from edge-transitive bipartite graphs. In Mathematica Slovaca, vol. 64, no.4, pp. 991-1006. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0253-3

Saedeleer, J., Leemans, D., Mixer, M., Pisanski, T. (2014). Core-free, rank two coset geometries from edge-transitive bipartite graphs. Mathematica Slovaca, 64(4), 991-1006. 0139-9918. DOI: https://doi.org/10.2478/s12175-014-0253-3